In the previous section, we derived the initial conditions for the radiation-dominated era, specifically, the initial values of the hypermagnetic helicity density and fermionic charge asymmetries [see Eq. (REF ) and Fig. REF ].
As outlined in the Introduction, these primordial charges set the stage for baryogenesis:
The asymmetries stored in the chiral fermions lead to wash-in leptogenesis, if they are not erased before RHN interactions become efficient; while the helicity stored in the hypermagnetic field can act as a source of baryon number, if it survives until the EWPT.
The survival of the primordial charges in the SM plasma is, however, endangered by several effects.
In addition to weak sphaleron processes, which seek to wash out any primordial baryon-plus-lepton number, we must pay attention to magnetic diffusion and the chiral plasma instability.
We will now discuss these two effects in the magnetohydrodynamics (MHD) approximation [1]}, [2]}, closely following the more detailed discussion in Ref. [3]}.
This will provide us with lower and upper bounds on the strength of the primordial hypermagnetic field from magnetic diffusion and the chiral plasma instability, respectively.
Remarkably, the range between these two bounds remains viable and can give rise to the correct BAU.
